An approximation theorem for sequences of linear strains and its applications

Zhang, Kewei

doi:10.1051/cocv:2004001

Zhang, Kewei

ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 2, pp. 224-242

Résumé

We establish an approximation theorem for a sequence of linear elastic strains approaching a compact set in $L^{1}$ by the sequence of linear strains of mapping bounded in Sobolev space $W^{1, p}$ . We apply this result to establish equalities for semiconvex envelopes for functions defined on linear strains via a construction of quasiconvex functions with linear growth.

MR Zbl

DOI : 10.1051/cocv:2004001

Classification : 26B25, 41A30, 49J45
Keywords: linear strains, maximal function, approximate sequences, quasiconvex envelope, quasiconvex hull

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     author = {Zhang, Kewei},
     title = {An approximation theorem for sequences of linear strains and its applications},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {224--242},
     year = {2004},
     publisher = {EDP Sciences},
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     number = {2},
     doi = {10.1051/cocv:2004001},
     mrnumber = {2083485},
     zbl = {1085.49017},
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     url = {https://www.numdam.org/articles/10.1051/cocv:2004001/}
}

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Zhang, Kewei. An approximation theorem for sequences of linear strains and its applications. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 2, pp. 224-242. doi: 10.1051/cocv:2004001

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